I assume you mean the latest possible POD? Probably before 1900, TBH; I can see a communist Japan (indeed, the militarists and nationalists were paranoid about Communist risings during the interwar period, and there was also some concern after WWII, although the US would never have allowed it), but a constitutional monarchy runs into the problems with the Qing, rising Chinese nationalism, and the tendency for most opposition to lean republican. A more competent Yuan Shikai might try and pull it off, but I can't imagine such a regime would have any legitimacy.
Ultimately constitutional monarchies are still around because they represent established monarchies that haven't gone through sufficient recent turmoil and revolution to get rid of them. It's hard to establish a new one, because you need to establish a new monarchic dynasty; that sort of thing was doable in the 19th century, but by the 20th century it's harder to take them seriously (Norway being, IIRC, the youngest constitutional monarchy, and even they were building on a combination of preexisting Swedish and Danish monarchies). Creating a new Chinese dynasty runs into that problem, and by 1900 it's really too late for the Qing to reform into a stable constitutional monarchy without collapsing.